Question: Simplify the following expression: $\sqrt{117}+\sqrt{13}-\sqrt{52}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{117}+\sqrt{13}-\sqrt{52}$ $= \sqrt{9 \cdot 13}+\sqrt{13}-\sqrt{4 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{13}+\sqrt{13}-\sqrt{4} \cdot \sqrt{13}$ $= 3\sqrt{13}+\sqrt{13}-2\sqrt{13}$ Finally, simplify by combining the terms. $= ( 3 + 1 - 2 )\sqrt{13} = 2\sqrt{13}$